MATH 431, FALL 2005- PROJECTS

This gives you an opportunity to explore in greater depth some differential equations arising in applications.

The goal is to use the theory and MATLAB plots to discover interesting features of each system,
including bifurcations, following the outline given in the relevant "exploration" section in the text.  You could also
try to track down the original paper where the model was first proposed (when a reference is given in
the text). ( This would help your grade, but is not required.) In addition to the relevant MATLAB plots, your
paper should include a brief introduction and a DISCUSSION section, with an interpretation of what the plots/results mean in
terms of the physical model.  ( I expect the papers to be typed.)

You will have a chance to present your results to the class in a short (15 min) talk.
Grading: paper (math): 45%; paper(organization): 35%; talk (coherence of presentation): 20%

It is OK (but again, not required) to work in groups of 2.
DEADLINE:  The papers are due 11/30 (exceptions noted below). Short talks on 11/30, 12/2, 12/5.

PROJECTS

1. Chemical reactions exhibiting oscillations (the Belusov- Zhabotinsky system)
Do 1-6 on p.231, including the relevant MATLAB plots. 

2.Species in competition including harvesting
Do 1-4 on p.253; include MATLAB plots and interpretation

3.The Fitzhugh-Nagumo equations: bifurcations
Do 1-9 p.272, including MATLAB plots and interpretation.

4. Non-Newtonian central force problems (paper due 12/5)
Do 1-9 p.297, including the relevant plots (choose the exponents so that change to xy coords is easy)

5.  Pendulum with constant forcing (paper due 12/5)
Do 1-5 (at least), including the relevant Matlab plots and interpretation.

6. Lorenz system (Ch. 14)
Summarize the content of  14-1, 14-2 in the introduction. Then do problem 2 (a to e) on
p. 129 of the MATLAB manual, following the  the method outlined on p.114-117.

7. Roessler system
Do 1,2  on p.324 , then Problem 10 (a to d) on p. 138 of the MATLAB manual
(suggestion: use the method described for the Lorenz system on o.114-117 of the manual)

Natural groups: the people doing 4 and 5 (resp. 6 and 7.) could work together.